TRIG RATIOS IN RIGHT TRIANGLES NOTES #1. otcn so. Exam le. Exam le. cos a. cos a = 2. Identify the side that is adjacent to ZZ. Z

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1 Geometry' Support Unit 4 Rigt Triangles Trig Notes Name Date REMEMBERING TRIG RATIOS IN RIGHT TRIANGLES NOTES #1 PYTHAGOREAN THEOREM enusv otcn so 2 2 IDENTIFY THE RATIOS l. Identify te side tat is opposite ZZ. 2. Identify te side tat is adjacent to ZZ. Z. Identify te ypotenuse. H z 4. Identify te side tat is opposite ZH.. Identify te side tat is adjacent to ZH. 6. Identify te ypotenuse. 1 In a rigt triangle, tere are several ratios tat can be created using trigonometry. Tere are tree main trig ratios and tente reciprocals of tose ratios. Ratio Definition orp Sine = Cosine = ad Exam le sin a = cos a 4 Exam le sin B = cos = Relationsi Between Ratios sin a = cos a = Tangent = OPP tan a = tan a =

2 Geometry Support Unit 4 Rigt Triangles Trig Notes Remembering Trigonometric Ratios: 'OH OAH TOA of 0 = opposite ypotenuse Old of e adjacent ypotenuse Hypo enuse Opposite 8f=O = opposite adjacent Adjacent sine. T ang nf opponft o pposif6 HyptcnUs1J Adjacent Examples: 00 ft 61 ft 00 ft 400 ft 00 ft 4 ft cos ft Tan % 0 1) : b 00 0 Oft Sin 0 : cos 0B Tan Sin Oft cos Tan

3 O Geometry Support Unit 4--Rigt Triangles Trig Notes Find te value of eac trigonometric ratio. Express your answer as a frqgtion in lowest terms. SINCE 2. SINC= (L B 0 40 a. B or vnolb off. cos c = 4. cos c = TAN A =. TAN x = fdgmpii

4 Geometry Support Unit 4 Rigt Triangles Trig Notes In te following problems, DRAW stick-man standing were te angle is and MARK eac given side as A (adjacent), O (opposite), or H (ypotenuse). Ten TELL wic TRIG RATIO you ave. You NOT be solving te problem for x (we aven't learned ow YET). l. Wic trig ratio is represented? B. COS COS x 2. Wic trig ratio is represented? B. COS C TAN x. Wic trig ratio is represented? B. COS Wic trig ratio is represented? B. COS Sin : C. TAN

5 Geometry Support Unit 4 Rigt Triangles Trig Notes Draw AABC were ZABC = 90 0, AB = BC = 1, and AC = Wat is tan C? usg 1 2. WatissinA? 1 AABC were LACB = 90 0, AC =, and CB = 12.. Wat is te lengt of AB? 26tlADl CL lbl 4. Wat is cosa? n 1. Watistan B? L ACAT were LATC = 90 0, CA =, and CT = Wat is te lengt of AT? 7- Wat issinc? : 4 n 8. Wat is tan cl 12 AABC were LB = 900 and sin A = Wat is te lengt of AB? L6bcDæ 46 1b is tan 11.WatiscosA?0.- _ 1b _ 4 20 AHAT were ZH = 900 and tan T = 12. Wat is te lengt of AT? 1. Wat is sin A? 14.Wat is cos T? I bbq IL 1 6

6 Geometry Support Name Unit 4: Rigt Triangle Trig Day 1 Practice Trig Ratios Date Practice find eac ratio and be sure to reduce, if possible Tanz x tant' 24 n simplify z 1 Sin X z PJi(YlflIfy Cos A B 40 Draw AABC were ZABC = 90 0, AB = 6, BC = 8, and AC =.. WatistanC? 4 6. Wat is sin A? Sin C tosirnqlify Draw AABC were ZACB 90 0, AC = 7, and CB = Wat is te lengt of AB? 4 8. Wat iscosa? 9. Wat is tan B? : 2 Draw ACAT were ZATC = 900, CA = 41, and CT = 9.. Wat is te lengt of AT? T IS 2 : c ll. Wat is sin C? Sin (J 12. Wat is tan A? AL n C' boo

7 Geometry Support Unit 4: Rigt Triangle Trig Practice Draw AABC were LB = 900 and sina = Wat is te lengt of AB? 14. Wat is tan A? 2bL b L : 7b b: WatiscosA?E- -M. 8 Draw AHAT were LH = 900 and tant = Wat is te lengt of AT? I 17. Wat is sin WatiscosT? 1 n Il 16 16) f In te following problems, using te angle tat is given, MARK eac given side as A (adjacent), O (opposite), or H (ypotenuse). Ten TELL wic TRIG RATIO you ave. You will NOT be solving te problem for x (we aven't learned ow YET). 19. Wic ratio is represented? s C. TAN Sin: O 9 ll m. Wic trig ratio is represented? D. SIN os F. TAN 20 x Wic trig ratio is represented? G. l. AN cos